Content uploaded by Imran Ullah Khan
Author content
All content in this area was uploaded by Imran Ullah Khan on Nov 09, 2017
Content may be subject to copyright.
International Journal of Innovative Technology and Exploring Engineering (IJITEE)
ISSN: 2278-3075, Volume-3, Issue-7, December 2013
165
The Performance Improvement of Long Range
Inter-relay Wireless Cooperative Network using
Three Time Slot TDMA based Protocol
Imranullah Khan, Tan Chon Eng
Abstract— Time division multiple access (TDMA) amplify and
forward based protocols for cooperative wireless networks have
been investigated previously by various researchers. However, the
analysis for these protocols is not considered for long range
cooperative wireless networks over Rician fading channel.
Therefore, the aim of this paper was to propose three time slot
TDMA based transmission protocol for inter-relay cooperative
wireless network with longer distances between source to relays
and destination as well as between relays to destination. It is
concluded that the proposed protocol shows less BER
performance for long range inter-relay cooperative network over
Rician fading channel as compared to two time slot long range
cooperative network. Moreover, the proposed protocol shows
better performance in terms of less BER values when the inter-
relay distance is minimum.
Keywords: Cooperative inter-relay wireless communication, AF
Protocol, TDMA, Path Loss Models, BER.
I. INTRODUCTION
The mobile radio channel suffers due to fading effects
during transmission of data from source to destination and
undergoes through several signal variations at destination. In
order to mitigate fading, diversity communication is used to
send the same data over independent fading paths (diversity
branches). There are some common techniques such as
micro diversity, macro diversity, space diversity, frequency
diversity and time diversity, which are used at the
transmitter and receiver to achieve diversity communication
[1]. The diversity achieved by the above methods tends to
increase the size, complexity and total power of the wireless
network devices. To solve this problem cooperative
diversity communication has been introduced recently.
In cooperative diversity communication the diversity is
achieved due to cooperation among users or relays, for
example, in case of two users or relays and one destination,
each user or relay is not only responsible for transmitting
their own information data, but the information of their
partner user or relay as well to the destination, virtually
seeking the advantages of MIMO spatial diversity [2-5].
Each user in cooperative diversity acts as a relay for another
user using either amplify and forward (AF) or decode and
forward protocol (DF) in order to transmit the information to
destination. In DF the relay decodes the received signal
from the source and forwards to destination, while, in AF
the relay amplifies the received signal from source and
forwards to destination [3], [6].
Manuscript received December, 2013.
Imran Ullah Khan, Faculty of Computer Science and Information
Technology University Malaysia Sarawak (UNIMAS) Malaysia
Tan Chog, Faculty of Computer Science and Information Technology
University Malaysia Sarawak (UNIMAS) Malaysia.
Cooperative communication solves the issues of size, cost,
and hardware limitations of multiple antennas [7].
Moreover, cooperative communication also helps to reduce
the effects of multi-path fading and increase capacity of
wireless channel as well as achieves high data rates [8-9].
Different multiple access techniques such as time-division
multiple access (TDMA), frequency division multiple access
(FDMA), and code division multiple access (CDMA) have
been proposed by researchers to achieve high diversity order
at destination [10-12].
In [13], the authors proposed three different two time
slots TDMA based transmission protocols. The protocols
implement varying degree of broadcasting and receive
collision at destination. In each protocol the relay either
amplify and forward or decode and forward the received
signal from source. In [14] a novel scheme of cooperative
network using three time slots is analyzed. The cooperative
network is based on data exchange between relays in the
third time slot in order to enhance the link performance
between relays and destination. In [15], the authors
proposed hybrid TDMA-FDMA based three time slots
protocol with inter-relay communication over Nakagami-m
fading channel. In [16] the authors proposed TDMA based
three time slot protocol with inter-relay communication over
Nakagami-m and Rician fading channels. In the first time
slot the source broadcasts to both the relays and destination.
in the second time slot the relays exchange their data as well
broadcasts to destination. In the 3rd time the relays
broadcasts the previously exchange data in the 2nd time slot
to destination. The source remains silent in the 2nd and 3rd
time slots and does not broadcasts to destination in these
slots.
To the best of our knowledge the BER analysis for inter-
relay communication using longer distances between source
to destination and relays as well as between relays to
destination has not been investigated. A path loss issue and
shadowing effects arises in case of longer distances between
source to destination and relays as well as between relays to
destination. In order to coup the path loss and shadowing
issues a proper path loss model is required during BER
analysis for inter-relay communication.
In our work, a three time slot TDMA based protocol
using path loss model with inter-relay communication is
proposed. BER analysis is investigated and repeated for
proposed model using 7 different selected path loss models.
The BER analysis results are then compared with the results
obtained from previously proposed protocol in [13]. It is
shown that the proposed protocol performs better in terms of
less BER as compared to two times slot protocol proposed
in [13].
The Performance Improvement of Long Range Inter-relay Wireless Cooperative Network using Three Time Slot
TDMA based Protocol
166
A. Description of Selected Path Loss Models
In wireless communication systems, the information is
transmitted between transmitter and receiver antenna by
electromagnetic waves. The signal strength of
electromagnetic waves weakens with respect to the distance
during propagation [17]. The difference of signal strengths
(power) from transmitter (source) to receiver (destination)
antenna is termed as path loss. Path loss (PL) of signals at
destination is generally determined by the use of different
models. The brief descriptions of some mostly used path
loss models in the literature are given in Table 1. Free Space
Path Loss (FSPL) model estimates the signal strength during
propagation from transmitter to receiver. The propagation
environment is assumed as free space [17-18]. HATA model
is applicable for a frequency range of 150-1500 MHz [17].
Different correction factors are being used for suburban and
rural environments [19]. HATA model used the value of
correction factor K from 35.94 for countryside and 40.94 for
deserts [20]. HATA model provides extension to Okumura
model for distances greater than 1km.
COST-231 HATA model is the extension of HATA
model. It is used for frequency ranges from 1500-2000
MHz. It incorporates the signal strength prediction up to
20km from transmitter to receiver with the transmitter
antenna height of 30 m to 200m and receiver antenna height
of 1m to 10m [21]. It is used to predict signal strength in all
environments. COST-231 WI model has separate equations
both for line of sight and non line of sight communications
regarding path loss estimation. However, the line of sight
equation is more appropriate in environments when the
communication is line of sight. ECC-33 model is one of the
most extensively used models, which is based on Okumura
model [22-23]. This model is widely used for urban
environments especially. Ericsson model is applied for all
the three environments such that urban, suburban and rural.
In Ericsson model, different parameters values are provided
for specific propagation environment [20].Lee model
operates around 900 MHz. This model includes adjustment
factors that can be adjusted to make the model more flexible
to different regions of propagation as compared to other
selected models [24].
II. SYSTEM MODEL
A cooperative network with two relays is considered as
shown in Fig. 1. The system model consists of source, two
relays and destination. The source (S), relay 1 (R1), relay2
(R2) and destination (D) all are equipped with single
antenna. The hSR1, hSR2, hR1D, hR2D, hR1R2 and hR2R1 are the
path gains of S to R1, S to R2, R1 to D, R2 to D , R1 to R2 and
R2 to R1 channels respectively. The amplify and forward
(AF) communication is used by the relays. Maximum ratio
combining (MRC) is used at the destination in order to
obtain BER at the destination.
Fig. 1: Inter-relay communication using three time slot protocol
TABLE 1 DESCRIPTION OF SELECTED PATH LOSS MODELS
A. Proposed Amplify and Forward (PAF) Three Time Slot
TDMA based Protocol
The system model used for three time slot proposed protocol
is shown in Fig. 1. In the first time slot the source broadcast
to destination, relay 1 and relay 2. In the second time slot
the source does not remain silent and broadcasts to
destination only. The R1 and R2 also broadcast to
destination as well as also exchange their data in the second
time slot. In the 3rd time slot R1 and R2 broadcast the
previously exchange data in the second time to destination.
The source keeps broadcasting to destination in the 3rd time
as well and does not remain silent. Table -2 shows the
summarized form of the proposed protocol.
TABLE 2 PROPOSED THREE TIMES SLOT TDMA BASED
PROTOCOL
The received signals at relay 1 relay 2 and destination in the
first time slot are
1SR
y
,
2SR
y
and
1,SD
y
respectively and
given by
11
1
1... SRSRSSR nshEPLy
22
1
2.. SRSRSSR nshEPLy
SDSDSSD nhEPLy..
1
1,
Where
1SR
d
,
2SR
d
hSR1 and
SD
d
are the distances be S to
International Journal of Innovative Technology and Exploring Engineering (IJITEE)
ISSN: 2278-3075, Volume-3, Issue-7, December 2013
167
R1, S to R2 and S to D channels respectively in the first
time slot. The PL indicates the path loss model.
The relays R1 and R2 receive the signals from the source in
the second time slot normalize the receive signals and
broadcast to destination. The received signals at the
destination from the R1, R2 and S at the destination in the
second time slot are
DR
y1
,
DR
y2
and
2,SD
y
, respectively
and given by
DR
SRs
SR
DRDR n
hE
y
hEPLy1
2
1
1
11
1
11
**.
DR
SRs
SR
DRDR n
hE
y
hEPLy2
2
2
2
22
1
21
**.
SDSDSSD nhEPLy..
1
2,
Where
DR
d1
,
DR
d2
and
SD
d
are the distances be R1 to D,
R2 to D and S to D channels respectively in the 2nd time
slot.
Similarly, both relays normalize the received signals from
source and exchange their data in the second time slot. The
received signals at R2 from R1 and at R1from R2 are
21RR
y
and
12RR
y
respectively and given by
21
2
1
1
211
1
21 1
**. RR
SRs
SR
RRRR n
hE
y
hEPLy
12
2
2
2
122
1
12 1
**. RR
SRs
SR
RRRR n
hE
y
hEPLy
Where
21RR
d
and
12RR
d
are the distances be R1 to R2, R2
to R1 and S to D channels respectively in the 2nd time slot.
In the 3rd time slot both R1 and R2 normalize the exchange
data received during 2nd time slot and broadcast to the
destination. The received signals at D from R1, at D from
R2 as well as at D from the source in the 3rd time slot
are
DR
y1
,
DR
y2
and
3,SD
y
respectively and given by
DR
RR
RR
RRDR n
hE
y
hEPLy1
2
211
21
211
1
11
**.
DR
RR
RR
RRDR n
hE
y
hEPLy2
2
122
12
122
1
21
**.
SDSDSSD nhEPLy..
1
3,
Maximum Ratio Combining (MRC) is used at destination in
order to extract the required information at destination. The
derived received information signal at D using MRC using
Matlab-7.8 is
D
y
and given by
**
*2
*12
*1
*1
*21
*22
** 2
*22
*1
*11
..
......
.....
SDSDSDSD
SRRRDRSRRRDRDR
SDSDSRDRDRSRDRDRD
hyhy
hhhyhhhy
hyhhyhhyy
III. SIMULATION AND RESULTS DISCUSSIONS
BER is used as performance metric and calculated at
destination for Inter-Relay Cooperative wireless network as
shown in Fig. 1. Bipolar Phase shift keying (BPSK)
modulation is used to modulate the signal. The additive
white Gaussian Noise (AWGN) with zero mean and
variance along with the Rayleigh channel and Rician fading
channels is used to make the channel noisy and multipath
respectively. In order to plot the BER 105 number of
symbols is used. Seven different path loss models (Lee
Model, Free Space Model, HATA Model, COST-231
HATA Model, ECC-33 Model, COST-231 WI Model and
Ericsson Model) were used by the proposed protocol.
Similarly, the proposed protocol was tested 7 times i.e., each
for a particular path loss model and to get the BER
regarding each specified path loss model. The protocol using
no path loss model while considering only distance between
the source to relays and destination as well as between
relays to destination is taken as a reference for comparison
in simulation. Line of sight communication (LOS) is
considered between source to relays and destination as well
as between relays to destination. The operating frequency
for each path loss model was fixed i.e., 1500MHz. In case of
COST-231 WI model LOS equation was considered. Both
relays were taken fixed and minimum inter-relay distance is
considered. The correction factor S is taken 10dB.
A. BER Analysis for system model for short distances
Consider that the distance between
DS
was fixed at
10m. Similarly, the distances between
1
RS
,
2
RS
DR1
and
DR2
were fixed at 5.59m. Moreover,
the distances between
21 RR
and
12 RR
were fixed
at 5 m. The transmitter and receiver antenna heights were
taken 3m.
The bit error rates for the proposed protocol using
different path loss models are shown in Fig. 1. It is observed
that the proposed amplify and forward protocol (PAFP)
COST-231 WI model shows heights BER. It is due to the
fact that COST-231 WI model has no adjustment factors for
antenna heights, antenna gains and frequency as compared
to other models. Similarly, the proposed protocol using
ECC-33 path loss model shows the second highest BER
compared to the proposed algorithm using other path loss
models. Owing to the fact that transmitter and receiver
antenna height correction factors are not effective at lower
transmitter and receiver heights. It is also observed during
the simulation that ECC-33 model is not more effective at
1500MHz and beyond 1500MHz frequency as compared to
other models. It is because this model has no additional
frequency adjustment factor incorporated to account the
effect of frequency.
It is indicated that the second lowest BER was shown by
proposed protocol using Ericson model as compared to other
models. It is because of the use of constants a0, a1 and a2 as
adjustment factors which are very effective for the
environment taken in the simulation. Moreover, an
additional adjustment factor for frequency is also used.
The lowest BER was shown by proposed protocol using
LEE path loss model as compared to other models. It is
because the LEE model has additional extra correction
factors like transmitter and receiver antenna gain correction
factors. It is also observed that during simulation the
transmitter and receiver antenna heights correction factors
The Performance Improvement of Long Range Inter-relay Wireless Cooperative Network using Three Time Slot
TDMA based Protocol
168
were more effective at lower transmitter and receiver
antenna heights as compared to other models.
B. BER Analysis for system model for longer distances
Consider that the distance between
DS
was fixed at
100m. Similarly, the distances between
1
RS
,
2
RS
DR1
and
DR2
were fixed at 55.9m. Moreover,
the distances between
21 RR
and
12 RR
were fixed
at 50 m. The operating frequency for each path loss model
was fixed again i.e., 1500MHz. It is expressed that when the
distance between source to relays and distance as well as
between relays to destination increases, the BER increases
However, the proposed protocol shows less BER
performance as compared to the protocol using no path loss
model as shown in Fig. 3. It is due to the fact that if the
distance increases the channel conditions become more
noisy and proposed protocol reduces the channel noise by
using the path loss model. It is also expressed that the
proposed protocol using Lee path loss model shows less
BER compared to the proposed protocol using other path
loss models. It is due to the fact that the adjustment or
correction factors (i.e., transmitter and receiver antennas as
well as frequency adjustment factors) for the current
simulation environment are more effective as compared to
the proposed algorithm using other path loss models.
Fig. 2: Bit error rate for PAFP using different path loss models vs SNR
Fig. 3: BER vs SNR for PAFP using different path loss models
Fig. 4: Comparison of PAF three time slot protocol and two times slot
protocol.
The proposed protocol is evaluated by doing comparison
with the BER results from TDMA based two time slot
protocol with inter-relay communication [13]. The proposed
protocol with the third extra time slot shows less BER
performance and high diversity order as compared to two
time slot transmission protocol as shown in Fig. 4.
IV. CONCLUSIONS
A three time slot TDMA based transmission protocol is
proposed and investigated for inter-relay cooperative
network with longer distances between source to relays and
destination as well as between relays to destination. It is
concluded that the proposed protocol shows better
performance in terms of less BER for long range inter-relay
cooperative network over Rician fading channel as
compared to two time slot long range cooperative network.
Our analysis also emphasize on analysis of BER when the
inter-relay distance is minimum.
Mathematical modeling for the proposed protocol in
order to design the channel matrix is left for future work.
Moreover, the proposed protocol can be further evaluated
with the three time slot decode and forward inter-relay
network.
V. ACKNOWLEDGEMENT
This research is conducted at faculty of computer science
and information technology, University Malaysia Sarawak
sponsored by Zamalah Postgraduate UNIMAS (ZPU).
REFERENCES
[1] A. Goldsmith, Wireless communications: Cambridge university
press, 2005.
[2] A. Sendonaris, et al., "User cooperation diversity. Part I. System
description," Communications, IEEE Transactions on, vol. 51, pp.
1927-1938, 2003.
[3] J. N. Laneman, et al., "Cooperative diversity in wireless networks:
Efficient protocols and outage behavior," Information Theory, IEEE
Transactions on, vol. 50, pp. 3062-3080, 2004.
[4] J. N. Laneman and G. W. Wornell, "Energy-efficient antenna
sharing and relaying for wireless networks," in Wireless
Communications and Networking Confernce, 2000. WCNC. 2000
IEEE, 2000, pp. 7-12.
[5] J. N. Laneman and G. W. Wornell, "Distributed space-time-coded
protocols for exploiting cooperative diversity in wireless networks,"
Information Theory, IEEE Transactions on, vol. 49, pp. 2415-2425,
2003.
[6] A. Kwasinski and K. R. Liu, "Source-Channel-Cooperation
Tradeoffs for Adaptive Coded Communications [Transactions
Papers]," Wireless Communications, IEEE Transactions on, vol. 7,
pp. 3347-3358, 2008.
[7] A. Nosratinia, et al., "Cooperative communication in wireless
International Journal of Innovative Technology and Exploring Engineering (IJITEE)
ISSN: 2278-3075, Volume-3, Issue-7, December 2013
169
networks," Communications Magazine, IEEE, vol. 42, pp. 74-80,
2004.
[8] P. A. Anghel and M. Kaveh, "Exact symbol error probability of a
cooperative network in a Rayleigh-fading environment," Wireless
Communications, IEEE Transactions on, vol. 3, pp. 1416-1421,
2004.
[9] R. Pabst, et al., "Relay-based deployment concepts for wireless and
mobile broadband radio," Communications Magazine, IEEE, vol.
42, pp. 80-89, 2004.
[10] V. Garg, Wireless Communications & Networking: Morgan
Kaufmann, 2010.
[11] H. Jiang, et al., "Quality-of-service provisioning and efficient
resource utilization in CDMA cellular communications," Selected
Areas in Communications, IEEE Journal on, vol. 24, pp. 4-15, 2006.
[12] J.-Z. Sun, et al., "Features in future: 4G visions from a technical
perspective," in Global Telecommunications Conference, 2001.
GLOBECOM'01. IEEE, 2001, pp. 3533-3537.
[13] R. U. Nabar, et al., "Fading relay channels: Performance limits and
space-time signal design," Selected Areas in Communications, IEEE
Journal on, vol. 22, pp. 1099-1109, 2004.
[14] S. A. Fares, et al., "A Novel Cooperative Relaying Network Scheme
with Inter-Relay Data Exchange," IEICE transactions on
communications, vol. 92, pp. 1786-1795, 2009.
[15] U. R. Tanoli, et al., "Hybrid TDMA-FDMA based inter-relay
communication in cooperative networks over Nakagami-m fading
channel," in Emerging Technologies (ICET), 2012 International
Conference on, 2012, pp. 1-5.
[16] U. Tanoli, et al., "Performance Analysis of Cooperative Networks
with Inter-Relay Communication over Nakagami-m and Rician
Fading Channels," International Journal on Multidisciplinary
sciences, 2012.
[17] V. Abhayawardhana, et al., "Comparison of empirical propagation
path loss models for fixed wireless access systems," in Vehicular
Technology Conference, 2005. VTC 2005-Spring. 2005 IEEE 61st,
2005, pp. 73-77.
[18] W. Joseph and L. Martens, "Performance evaluation of broadband
fixed wireless system based on IEEE 802.16," in Wireless
Communications and Networking Conference, 2006. WCNC 2006.
IEEE, 2006, pp. 978-983.
[19] C. Action, Digital Mobile Radio Towards Future Generation
Systems: Final Report: Directorate General Telecommunications,
Information Society, Information Market, and Exploitation
Research, 1999.
[20] M. Shahajahan and A. A. Hes-Shafi, "Analysis of propagation
models for WiMAX at 3.5 GHz," Department of Electrical
Engineering Blekinge Institute of Technology, 2009.
[21] T. S. Priya, "Optimised COST-231 Hata Models for WiMAX Path
Loss Prediction in Suburban and Open Urban Environments,"
Modern Applied Science, vol. 4, p. P75, 2010.
[22] V. Erceg, et al., "Channel models for fixed wireless applications,"
ed: IEEE, 2001.
[23] Y. Okumura, et al., "Field strength and its variability in VHF and
UHF land-mobile radio service," Rev. Elec. Commun. Lab, vol. 16,
pp. 825-73, 1968.
[24] W. Heisenberg, "Lee model and quantisation of non linear field
equations," Nuclear Physics, vol. 4, pp. 532-563, 1957.
[1] A. Goldsmith, Wireless communications: Cambridge university
press, 2005.
[2] A. Sendonaris, et al., "User cooperation diversity. Part I. System
description," Communications, IEEE Transactions on, vol. 51, pp.
1927-1938, 2003.
[3] J. N. Laneman, et al., "Cooperative diversity in wireless networks:
Efficient protocols and outage behavior," Information Theory, IEEE
Transactions on, vol. 50, pp. 3062-3080, 2004.
[4] J. N. Laneman and G. W. Wornell, "Energy-efficient antenna
sharing and relaying for wireless networks," in Wireless
Communications and Networking Confernce, 2000. WCNC. 2000
IEEE, 2000, pp. 7-12.
[5] J. N. Laneman and G. W. Wornell, "Distributed space-time-coded
protocols for exploiting cooperative diversity in wireless networks,"
Information Theory, IEEE Transactions on, vol. 49, pp. 2415-2425,
2003.
[6] A. Kwasinski and K. R. Liu, "Source-Channel-Cooperation
Tradeoffs for Adaptive Coded Communications [Transactions
Papers]," Wireless Communications, IEEE Transactions on, vol. 7,
pp. 3347-3358, 2008.
[7] A. Nosratinia, et al., "Cooperative communication in wireless
networks," Communications Magazine, IEEE, vol. 42, pp. 74-80,
2004.
[8] P. A. Anghel and M. Kaveh, "Exact symbol error probability of a
cooperative network in a Rayleigh-fading environment," Wireless
Communications, IEEE Transactions on, vol. 3, pp. 1416-1421,
2004.
[9] R. Pabst, et al., "Relay-based deployment concepts for wireless and
mobile broadband radio," Communications Magazine, IEEE, vol.
42, pp. 80-89, 2004.
[10] V. Garg, Wireless Communications & Networking: Morgan
Kaufmann, 2010.
[11] H. Jiang, et al., "Quality-of-service provisioning and efficient
resource utilization in CDMA cellular communications," Selected
Areas in Communications, IEEE Journal on, vol. 24, pp. 4-15, 2006.
[12] J.-Z. Sun, et al., "Features in future: 4G visions from a technical
perspective," in Global Telecommunications Conference, 2001.
GLOBECOM'01. IEEE, 2001, pp. 3533-3537.
[13] R. U. Nabar, et al., "Fading relay channels: Performance limits and
space-time signal design," Selected Areas in Communications, IEEE
Journal on, vol. 22, pp. 1099-1109, 2004.
[14] S. A. Fares, et al., "A Novel Cooperative Relaying Network Scheme
with Inter-Relay Data Exchange," IEICE transactions on
communications, vol. 92, pp. 1786-1795, 2009.
[15] U. R. Tanoli, et al., "Hybrid TDMA-FDMA based inter-relay
communication in cooperative networks over Nakagami-m fading
channel," in Emerging Technologies (ICET), 2012 International
Conference on, 2012, pp. 1-5.
[16] U. Tanoli, et al., "Performance Analysis of Cooperative Networks
with Inter-Relay Communication over Nakagami-m and Rician
Fading Channels," International Journal on Multidisciplinary
sciences, 2012.
[17] V. Abhayawardhana, et al., "Comparison of empirical propagation
path loss models for fixed wireless access systems," in Vehicular
Technology Conference, 2005. VTC 2005-Spring. 2005 IEEE 61st,
2005, pp. 73-77.
[18] W. Joseph and L. Martens, "Performance evaluation of broadband
fixed wireless system based on IEEE 802.16," in Wireless
Communications and Networking Conference, 2006. WCNC 2006.
IEEE, 2006, pp. 978-983.
[19] C. Action, Digital Mobile Radio Towards Future Generation
Systems: Final Report: Directorate General Telecommunications,
Information Society, Information Market, and Exploitation
Research, 1999.
[20] M. Shahajahan and A. A. Hes-Shafi, "Analysis of propagation
models for WiMAX at 3.5 GHz," Department of Electrical
Engineering Blekinge Institute of Technology, 2009.
[21] T. S. Priya, "Optimised COST-231 Hata Models for WiMAX Path
Loss Prediction in Suburban and Open Urban Environments,"
Modern Applied Science, vol. 4, p. P75, 2010.
[22] V. Erceg, et al., "Channel models for fixed wireless applications,"
ed: IEEE, 2001.
[23] Y. Okumura, et al., "Field strength and its variability in VHF and
UHF land-mobile radio service," Rev. Elec. Commun. Lab, vol. 16,
pp. 825-73, 1968.
[24] W. Heisenberg, "Lee model and quantisation of non linear field
equations," Nuclear Physics, vol. 4, pp. 532-563, 1957.